Baseball Therapy

Wild-Card Game Theory

It's the time of year when the races to the top start to tighten, and for lovers of chaos and mayhem (like me!), we can start dreaming of scenarios that involve ties and one-game playoffs. And this year, as an added bonus, we're guaranteed to get two games of win-or-you’re-out thanks to the new wild-card play-in game. My favorite scenario—far-fetched at this point, but it could happen—is one in which the Orioles, Rays, and Yankees finish tied atop the AL East, with the same record as the Angels and Tigers, and all one game behind Oakland for the second wild-card spot. Texas wins the AL West, and the White Sox win the AL Central. Just for giggles, we can have the Rangers tie the A's so that they can battle to decide who wins the AL West and who gets the first wild card.

From my understanding, the Orioles, Rays, and Yankees would have to go through a three-team mini-tournament to hash out the AL East. The two losers would then still have to fight with the Angels and the Tigers for the last wild-card spot and would engage in a four-team tournament for the right to play a one-off with the A's/Rangers loser. In theory, one of those AL East teams could end up playing four(!) extra games—against a different team every day—and that's before getting to the actual wild-card one-off with the Rangers/A's loser. While everyone else is blowing out their bullpens, the White Sox could conceivably sit back, rest, and watch some really compelling baseball from the comfort of their clubhouse for most of a week.

As wonderful as that would be, let's instead shift to a more realistic scenario. Baltimore, despite the extensive amount of rain that I and others have attempted to pour on their parade, manages to finish tied with the Yankees for the AL East crown, and with both teams having a good enough record that the loser of the one-game playoff would still make the wild-card game, likely against Oakland. What should the Orioles do? They face a showdown with the Yankees, likely with CC Sabathia on the mound. If the Orioles win, great for them! If they lose, it's not the end of the world. They play Oakland the next day in the wild-card game. They have to win only one of the two, and if they do, they're into the ALDS. It's not a bad spot to be in, really.

Let's focus on the Orioles for a moment in this win-one-of-two scenario and think strategically. To get to this point, the Orioles have probably been sprinting for the last week or so, asking hitters to forego off-days, asking relievers to go an extra out or two past their usual quota, and perhaps throwing a starter on short rest here or there. Guys are tired. Baseball is a game of attrition, after all. The standard refrain will be that you can rest in November, but maybe it might be the right strategic decision to take a little break—by punting the one-game playoff for the division crown.

The usual strategy for the one-game division playoff would be to start your ace, if available, even on short rest, prepare your high-leverage relievers to go two innings, and generally max out all available resources to win this game. If you win, you end up in the ALDS (and can claim in 20 years that you won your division. Woohoo!) If you lose, your ace is unavailable for the wild-card game. Your high leverage relievers all have tired arms. Your hitters have to fly across the country to Oakland to face a bunch of guys who watched your game on TV yesterday. You maxed everything out yesterday and are going to face a team that had an off-day. Good luck.

What if, instead, the Orioles sent a skeleton crew of backups to face the Yankees? The divisional playoff counts as a regular-season game, so the expanded September rosters are still available. Cobble together some bench guys, those Triple-A callups at whom you’ve wanted to take a look, your fifth starter, a couple of "arms" to cover any relief innings, and send them out—on national TV—to get humiliated. (If they magically win, that's pure frosting.)

The "real" team spends the day golfing and catches an early flight out to California. The next day, everyone's on full rest and ready to go for the biggest game of the season. And if you win that one, you still end up in the ALDS. Sure, the O's get only one chance instead of two, but the way the schedule works, they might be able to marshal their full resources for only one game anyway. Why not pick the one when everyone can be a little better rested?

And then there's the issue of whom you would rather face with everything on the line: the Yankees or the A's? There comes a point where this might actually make sense. It's like playing two sequential hands of poker, only knowing in advance what your cards will be on the second hand. If you don't have a lot of chips, doesn't it make sense to bet harder on the better hand? September makes things that look silly in July seem sensible.

(Credit where due: I was inspired by the article by Max Marchi linked directly above. Also, I believe that BP alums Joe Sheehan and Rany Jazayerli had a discussion of these types of possibilities where teams might actually have an incentive to lose, in a slightly different context, on their podcast.)

Okay, fantasy over. Here's why this would never actually happen, even if it should.

First off, even if I could make the case that punting the game makes sense, this would (correctly?) be viewed as the Orioles ducking the Yankees, and masculine pride has a thing about not backing down, even when it's the correct course of action. Second off, we're talking about a team semi-intentionally trying to lose a game that decides a playoff participant. The commissioner's office might take an interest in that not actually happening. Third, if the plan backfired, it would create a backlash on an order that has never been seen before. Come to think of it, even if it works...

Even throwing those objections away, there's another more logical reason why a team would never actually do this. Suppose the Orioles telegraphed their intentions, most likely through announcing their starting pitcher. Suddenly, the Yankees are looking at "wasting" Sabathia's start on a game where the other team is clearly not even trying and the game is not really a must-win. The Yankees might figure that they can get by with some other starter, hold Sabathia back a day, and get him some extra rest. In some sense, the Yankees might be seen as punting here. But now, if the O's play their "real" team, the game looks a lot more winnable—maybe a better bet than going to Oakland, even with the extra rest. But, if the Orioles are going to play their real lineup, the Yankees might go back to Sabathia. Which could lead the Orioles to go back to their Triple-A lineup. This turns into a bizarre cat-and-mouse game really quickly. We've entered the land of game theory.

There's probably a master's thesis in the calculus that would dictate what the actual best decision would be for both sides. The reality is that even if two teams got to the point where they were entertaining such thoughts, the tie-breaker in this ambiguity would be the cultural expectation that no one backs down. And a call from the commissioner's office. Both teams would probably max out for this game and let tomorrow come as it may.

The odd denoument to this thought exercise is this: suppose that the Yankees and Orioles get into the game, and by the fourth inning, someone is winning 11-0. The logical thing to do for the losing team would be to fold up, not use any important bullpen resources to try to chase the game, and maybe get the regulars off the field for an earlier flight (and arrival time) to the next game. And either Joe Girardi or Buck Showalter would be recognized for the wisdom of not throwing good money after bad. No one would consider it a punt because the situation is essentially hopeless for this game. But what if those calculations had happened a day earlier?

The problem with your thought experiment at the end is that the score is 11-0, so the game is over. Pre-game, with two teams making a reasonable effort, it's pretty unusual for one team to be more than about 70% to win against another MLB team.

My point there is that at 11-0, the math is pretty obvious and the logical thing to do is to punt the rest of the game and live to see tomorrow. But let's say that you do some math the day before and realize that the best idea is to punt the whole game. In both cases, you're giving up. It's just a matter of when. Would the Yankees or Orioles or whatever team did it be hailed as wise or fools?

1) There is no healthy "ace" on the Orioles. The starters are all pretty similarly bad.

2) Even assuming there was an ace a full 1.0 RA/9 better than than the next best pitcher, the math behind your theory doesn't work. Assume the following:
By fully punting the game (starting AAA scrubs), you have a 10% chance of winning game 1 (of these 2 theoretical games).
With your ace on the mound and normal batters vs. Sabathia, you have a 40% chance of winning game 1.
If you play Oakland with your ace and an extra-rested team, you have 50% chance of winning game 2.
With a tired team and your #2 pitcher vs. Oakland, you have a 40% chance of winning (8% delta due to SP downgrade of 1.00 RA9, and 2% due to less rest for team).

Not even close, and that is assuming you have a true ace. You can even make odds of beating Sabathia 30% (with your tired ace and team), and it still is not advantageous to punt a game.

Game theory certainly applies when deciding whom to start in a particular game of a sequence, as Marchi has already pointed out (http://www.baseballprospectus.com/article.php?articleid=18263), but frankly that has always been true for postseason situations. The concept of not sending your best hitters in a given game would not make sense in any realistic situation in my opinion.

Love this, although I'd argue that a 9% swing is in fact pretty close, especially given how hypothetical your assumptions are.

e.g., what if the chance of winning while punting was 20%? That would push the chances of making the ALDS while punting over top. And actually, ~20% would probably be more reasonable since according to WAR/WARP, a roster of replacement players should win ~32% of their games- but should probably take a hit since they're playing a postseason-quality team.

I would gladly admit that the circumstances that would need to come about are a little far-fetched. But let's say that the Yankees would start CC while the A's, due to having to sprint through the last week of the season, would only have some #4 guy available. And let's give the O's Justin Verlander.

I meant this piece to be more theoretical than anything. My ultimate thought is that there exists some set of not-impossible circumstances in which punting makes logical sense.

Right. Under these circumstances - where teams are tied for first, but both are assured of a wild card spot - you have mad e a good case that they do not push their ace out there on short rest for the division title play-off and just let him pitch the wild card play-off, if not the opening game of the Division Series if they happen to win the division title play-off. However, as for resting starting position players, I strongly doubt the benefit is worth the cost of increasing your chances of having to play an extra elimination game - unless it is night game for the division title followed the next afternoon by the wild card play-off, in which case you might rest your catcher.

Relievers under this scenario would probably be treated as they would for a clinching play-off game, but not a 7th game of a series.

The scenario I was mulling two weeks ago (when it was still possible) was NY/OAK/BAL tying for best AL record. Obviously, all will make the playoffs in this case as the division winner and both Wild Cards.

During the division champion playoff phase, there's the weird two game set where one team (randomly?) gets a bye before visiting the winner of the first game. So teams A and B need to play two games to win the division, team C only one. It seems like it would clearly be advantageous to lose the first game (and get a day off before the Wild-Card play in game) compared to winning the first game and losing the second (and then have no time off before the WC game). It seems to me that both teams in the first game have a strong reason not to pitch their best pitcher, since going 1-1 not only leaves you less rested than going 0-1 but gains no actual advantage. It does seem clear that winning the division does carry an advantage over winning the Wild Card, though naturally I haven't done any of the math for any of this.

It's actually not random who gets the bye. There's a set of tie-breakers to determine seeding (starts with head-to-head). The top seed gets to pick whether they want to play two home games (beat both #2 and #3 at home) to advance or one road game (make #2 and #3) play, and then go to the winner's stadium for a winner-take-all game.

Shouldn't the Orioles play the divisional tiebreaker game in the same fashion as any other regular season game? That is, don't overextend the bullpen to win the Yankees game at all costs? That way, they can still have key relief pitchers available for a possible Wild Card game vs. the A's? If they burn up all the good relief pitching vs. the Yankees, they have less of a chance vs. the A's.

I just want to interrupt to thank Bud Selig for making this possible, and mostly for recognizing that a wildcard team should merit the first two of a five-game series on its home field against the pretender that got into this by lucking out to top its division. Personally, I'd like to invite Mr. Selig to my grandson's first birthday party -- as the pinata.

Maybe this is a stupid question: one-game playoffs technically count as regular season games, no? Stats go towards regular season, records end up with 163 games played, etc.

So say Chicago wins the central and Texas wins the west, and NYY, BAL, DET, and OAK all end up with the same record, e.g. 92-70. Now NYY and BAL have to play a one-game playoff for the east. Doesn't the loser technically finish with a record of 92-71 for the season - 1/2 game out of the wild cards, which would go to DET and OAK by default?

MLB specifically ruled on this one a few years ago that in the event of a "mixed" three way tie where you are tied for both the division and (at the time the only) Wild Card, being in game #163 for the division will not knock you out of the Wild Card tie.

I was thinking an interesting and fairly realistic scenario will be when a team has clinched a wild card (let's say Oakland) and faces one of two teams vying for their division title, with the loser getting the other wild card (let's say Baltimore and New York). Oakland might choose to basically forfeit their game(s), so as to face the team they weren't playing in the WC playoff. This would make perfect sense if the choice was between facing Sabathia or whoever the Orioles might throw.

A similar scenario occurred in 1996 when San Diego and LA were tied going into the final game of the regular season. Both teams had already clinched playoff spots but neither could gain home field. The teams played the game like a spring training game, using reserves liberally (San Diego won). It ultimately was of no consequence as San Diego lost to St. Louis and LA lost to Atlanta.